Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.04407 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914093139492864 |
|---|---|
| author | Dvořáková, Lubomíra Kreczman, Savinien Pelantová, Edita |
| author_facet | Dvořáková, Lubomíra Kreczman, Savinien Pelantová, Edita |
| contents | We study a class of infinite words $x_k$ , where $k$ is a positive integer, recently introduced by J. Shallit. This class includes the Thue-Morse sequence $x_1$, the Fibonacci-Thue-Morse sequence $x_2$, and the Allouche-Johnson sequence $x_3$. Shallit stated and for $k = 3$ proved two conjectures on properties of $x_k$. The first conjecture concerns the factor complexity, the second one the critical exponent of these words. We confirm the validity of both conjectures for every $k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04407 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On two conjectures of Shallit about Thue-Morse-like sequences Dvořáková, Lubomíra Kreczman, Savinien Pelantová, Edita Combinatorics 68R15 G.2.1 We study a class of infinite words $x_k$ , where $k$ is a positive integer, recently introduced by J. Shallit. This class includes the Thue-Morse sequence $x_1$, the Fibonacci-Thue-Morse sequence $x_2$, and the Allouche-Johnson sequence $x_3$. Shallit stated and for $k = 3$ proved two conjectures on properties of $x_k$. The first conjecture concerns the factor complexity, the second one the critical exponent of these words. We confirm the validity of both conjectures for every $k$. |
| title | On two conjectures of Shallit about Thue-Morse-like sequences |
| topic | Combinatorics 68R15 G.2.1 |
| url | https://arxiv.org/abs/2506.04407 |